TMatrixTUtils.h

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// @(#)root/matrix:$Id$
// Authors: Fons Rademakers, Eddy Offermann   Nov 2003

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

#ifndef ROOT_TMatrixTUtils
#define ROOT_TMatrixTUtils

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// Matrix utility classes.                                              //
//                                                                      //
// Templates of utility classes in the Linear Algebra Package.          //
// The following classes are defined here:                              //
//                                                                      //
// Different matrix views without copying data elements :               //
//   TMatrixTRow_const        TMatrixTRow                               //
//   TMatrixTColumn_const     TMatrixTColumn                            //
//   TMatrixTDiag_const       TMatrixTDiag                              //
//   TMatrixTFlat_const       TMatrixTFlat                              //
//   TMatrixTSub_const        TMatrixTSub                               //
//   TMatrixTSparseRow_const  TMatrixTSparseRow                         //
//   TMatrixTSparseDiag_const TMatrixTSparseDiag                        //
//                                                                      //
//   TElementActionT                                                    //
//   TElementPosActionT                                                 //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

#include "TMatrixTBase.h"

#include <initializer_list>

template<class Element> class TVectorT;
template<class Element> class TMatrixT;
template<class Element> class TMatrixTSym;
template<class Element> class TMatrixTSparse;

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TElementActionT                                                      //
//                                                                      //
// A class to do a specific operation on every vector or matrix element //
// (regardless of it position) as the object is being traversed.        //
// This is an abstract class. Derived classes need to implement the     //
// action function Operation().                                         //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TElementActionT {

#ifndef __CINT__
friend class TMatrixTBase  <Element>;
friend class TMatrixT      <Element>;
friend class TMatrixTSym   <Element>;
friend class TMatrixTSparse<Element>;
friend class TVectorT      <Element>;
#endif

protected:
   virtual ~TElementActionT() { }
   virtual void Operation(Element &element) const = 0;

private:
   TElementActionT& operator=(const TElementActionT<Element> &) {return *this;}
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TElementPosActionT                                                   //
//                                                                      //
// A class to do a specific operation on every vector or matrix element //
// as the object is being traversed. This is an abstract class.         //
// Derived classes need to implement the action function Operation().   //
// In the action function the location of the current element is        //
// known (fI=row, fJ=columns).                                          //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TElementPosActionT {

#ifndef __CINT__
friend class TMatrixTBase  <Element>;
friend class TMatrixT      <Element>;
friend class TMatrixTSym   <Element>;
friend class TMatrixTSparse<Element>;
friend class TVectorT      <Element>;
#endif

protected:
   mutable Int_t fI; // i position of element being passed to Operation()
   mutable Int_t fJ; // j position of element being passed to Operation()
   virtual ~TElementPosActionT() { }
   virtual void Operation(Element &element) const = 0;

private:
   TElementPosActionT<Element>& operator=(const TElementPosActionT<Element> &) {return *this;}
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTRow_const                                                    //
//                                                                      //
// Template class represents a row of a TMatrixT/TMatrixTSym            //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTRow_const {

protected:
   const TMatrixTBase<Element> *fMatrix;  //  the matrix I am a row of
         Int_t                  fRowInd;  //  effective row index
         Int_t                  fInc;     //  if ptr = @a[row,i], then ptr+inc = @a[row,i+1]
   const Element               *fPtr;     //  pointer to the a[row,0]

public:
   TMatrixTRow_const() { fMatrix = 0; fRowInd = 0; fInc = 0; fPtr = 0; }
   TMatrixTRow_const(const TMatrixT   <Element> &matrix,Int_t row);
   TMatrixTRow_const(const TMatrixTSym<Element> &matrix,Int_t row);
  TMatrixTRow_const(const TMatrixTRow_const<Element>& trc):
    fMatrix(trc.fMatrix), fRowInd(trc.fRowInd), fInc(trc.fInc), fPtr(trc.fPtr) { }
  TMatrixTRow_const<Element>& operator=(const TMatrixTRow_const<Element>& trc) {
    if(this != &trc) { fMatrix=trc.fMatrix; fRowInd=trc.fRowInd; fInc=trc.fInc; fPtr=trc.fPtr; } return *this;}
   virtual ~TMatrixTRow_const() { }

   inline const TMatrixTBase<Element> *GetMatrix  () const { return fMatrix; }
   inline       Int_t                  GetRowIndex() const { return fRowInd; }
   inline       Int_t                  GetInc     () const { return fInc; }
   inline const Element               *GetPtr     () const { return fPtr; }
   inline const Element               &operator   ()(Int_t i) const {
      if (!fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(fMatrix->IsValid());
      const Int_t acoln = i-fMatrix->GetColLwb();
      if (acoln < fMatrix->GetNcols() && acoln >= 0)
         return fPtr[acoln];
      else {
         Error("operator()","Request col(%d) outside matrix range of %d - %d",
                            i,fMatrix->GetColLwb(),fMatrix->GetColLwb()+fMatrix->GetNcols());
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element               &operator   [](Int_t i) const { return (*(const TMatrixTRow_const<Element> *)this)(i); }

   ClassDef(TMatrixTRow_const,0)  // Template of General Matrix Row Access class
};

template<class Element> class TMatrixTRow : public TMatrixTRow_const<Element> {

public:
   TMatrixTRow() {}
   TMatrixTRow(TMatrixT   <Element> &matrix,Int_t row);
   TMatrixTRow(TMatrixTSym<Element> &matrix,Int_t row);
   TMatrixTRow(const TMatrixTRow<Element> &mr);

   inline Element *GetPtr() const { return const_cast<Element *>(this->fPtr); }

   inline const Element &operator()(Int_t i) const {
      if (!this->fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(this->fMatrix->IsValid());
      const Int_t acoln = i-this->fMatrix->GetColLwb();
      if (acoln < this->fMatrix->GetNcols() || acoln >= 0)
         return (this->fPtr)[acoln];
      else {
         Error("operator()","Request col(%d) outside matrix range of %d - %d",
                            i,this->fMatrix->GetColLwb(),this->fMatrix->GetColLwb()+this->fMatrix->GetNcols());
         return TMatrixTBase<Element>::NaNValue();
     }
   }
   inline       Element &operator()(Int_t i) {
      if (!this->fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(this->fMatrix->IsValid());
      const Int_t acoln = i-this->fMatrix->GetColLwb();
      if (acoln < this->fMatrix->GetNcols() && acoln >= 0)
         return (const_cast<Element *>(this->fPtr))[acoln];
      else {
         Error("operator()","Request col(%d) outside matrix range of %d - %d",
                            i,this->fMatrix->GetColLwb(),this->fMatrix->GetColLwb()+this->fMatrix->GetNcols());
         //return (const_cast<Element *>(this->fPtr))[0];
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element &operator[](Int_t i) const { return (*(const TMatrixTRow<Element> *)this)(i); }
   inline       Element &operator[](Int_t i)       { return (*(      TMatrixTRow<Element> *)this)(i); }

   void Assign (Element  val);
   void operator= (std::initializer_list<Element>  l);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTRow_const<Element> &r);
   TMatrixTRow<Element>& operator=(const TMatrixTRow      <Element> &r) { operator=((TMatrixTRow_const<Element> &)r); return *this;}
   void operator=(const TVectorT         <Element> &vec);

   void operator+=(const TMatrixTRow_const<Element> &r);
   void operator*=(const TMatrixTRow_const<Element> &r);

   ClassDef(TMatrixTRow,0)  // Template of General Matrix Row Access class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTColumn_const                                                 //
//                                                                      //
// Template class represents a column of a TMatrixT/TMatrixTSym         //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTColumn_const {

protected:
   const TMatrixTBase<Element> *fMatrix;  //  the matrix I am a column of
         Int_t                  fColInd;  //  effective column index
         Int_t                  fInc;     //  if ptr = @a[i,col], then ptr+inc = @a[i+1,col]
   const Element               *fPtr;     //  pointer to the a[0,col] column

public:
   TMatrixTColumn_const() { fMatrix = 0; fColInd = 0; fInc = 0; fPtr = 0; }
   TMatrixTColumn_const(const TMatrixT   <Element> &matrix,Int_t col);
   TMatrixTColumn_const(const TMatrixTSym<Element> &matrix,Int_t col);
   TMatrixTColumn_const(const TMatrixTColumn_const<Element>& trc):
     fMatrix(trc.fMatrix), fColInd(trc.fColInd), fInc(trc.fInc), fPtr(trc.fPtr) { }
   TMatrixTColumn_const<Element>& operator=(const TMatrixTColumn_const<Element>& trc) {
     if(this != &trc) { fMatrix=trc.fMatrix; fColInd=trc.fColInd; fInc=trc.fInc; fPtr=trc.fPtr; } return *this;}
   virtual ~TMatrixTColumn_const() { }

   inline const TMatrixTBase <Element> *GetMatrix  () const { return fMatrix; }
   inline       Int_t                   GetColIndex() const { return fColInd; }
   inline       Int_t                   GetInc     () const { return fInc; }
   inline const Element                *GetPtr     () const { return fPtr; }
   inline const Element                &operator   ()(Int_t i) const {
      if (!this->fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(fMatrix->IsValid());
      const Int_t arown = i-fMatrix->GetRowLwb();
      if (arown < fMatrix->GetNrows() && arown >= 0)
         return fPtr[arown*fInc];
      else {
         Error("operator()","Request row(%d) outside matrix range of %d - %d",
                            i,fMatrix->GetRowLwb(),fMatrix->GetRowLwb()+fMatrix->GetNrows());
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element                &operator [](Int_t i) const { return (*(const TMatrixTColumn_const<Element> *)this)(i); }

   ClassDef(TMatrixTColumn_const,0)  // Template of General Matrix Column Access class
};

template<class Element> class TMatrixTColumn : public TMatrixTColumn_const<Element> {

public:
   TMatrixTColumn() {}
   TMatrixTColumn(TMatrixT   <Element>&matrix,Int_t col);
   TMatrixTColumn(TMatrixTSym<Element>&matrix,Int_t col);
   TMatrixTColumn(const TMatrixTColumn <Element>&mc);

   inline Element *GetPtr() const { return const_cast<Element *>(this->fPtr); }

   inline const Element &operator()(Int_t i) const {
      if (!this->fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(this->fMatrix->IsValid());
      const Int_t arown = i-this->fMatrix->GetRowLwb();
      if (arown < this->fMatrix->GetNrows() && arown >= 0)
         return (this->fPtr)[arown*this->fInc];
      else {
         Error("operator()","Request row(%d) outside matrix range of %d - %d",
                            i,this->fMatrix->GetRowLwb(),this->fMatrix->GetRowLwb()+this->fMatrix->GetNrows());
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline       Element &operator()(Int_t i) {
      if (!this->fMatrix) return TMatrixTBase<Element>::NaNValue();
      R__ASSERT(this->fMatrix->IsValid());
      const Int_t arown = i-this->fMatrix->GetRowLwb();

      if (arown < this->fMatrix->GetNrows() && arown >= 0)
         return (const_cast<Element *>(this->fPtr))[arown*this->fInc];
      else {
         Error("operator()","Request row(%d) outside matrix range of %d - %d",
                            i,this->fMatrix->GetRowLwb(),this->fMatrix->GetRowLwb()+this->fMatrix->GetNrows());
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element &operator[](Int_t i) const { return (*(const TMatrixTColumn<Element> *)this)(i); }
   inline       Element &operator[](Int_t i)       { return (*(      TMatrixTColumn<Element> *)this)(i); }

   void Assign (Element val);
   // keep it for backward compatibility (but it has been removed for TMatrixTRow)
   void operator= (Element val) { return Assign(val); }
   void operator= (std::initializer_list<Element>  l);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTColumn_const<Element> &c);
   TMatrixTColumn<Element>& operator=(const TMatrixTColumn <Element> &c) { operator=((TMatrixTColumn_const<Element> &)c); return *this;}
   void operator=(const TVectorT            <Element> &vec);

   void operator+=(const TMatrixTColumn_const<Element> &c);
   void operator*=(const TMatrixTColumn_const<Element> &c);

   ClassDef(TMatrixTColumn,0)  // Template of General Matrix Column Access class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTDiag_const                                                   //
//                                                                      //
// Template class represents the diagonal of a TMatrixT/TMatrixTSym     //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTDiag_const {

protected:
   const TMatrixTBase<Element> *fMatrix;  //  the matrix I am the diagonal of
         Int_t                  fInc;     //  if ptr=@a[i,i], then ptr+inc = @a[i+1,i+1]
         Int_t                  fNdiag;   //  number of diag elems, min(nrows,ncols)
   const Element               *fPtr;     //  pointer to the a[0,0]

public:
   TMatrixTDiag_const() { fMatrix = 0; fInc = 0; fNdiag = 0; fPtr = 0; }
   TMatrixTDiag_const(const TMatrixT   <Element> &matrix);
   TMatrixTDiag_const(const TMatrixTSym<Element> &matrix);
   TMatrixTDiag_const(const TMatrixTDiag_const<Element>& trc):
    fMatrix(trc.fMatrix), fInc(trc.fInc), fNdiag(trc.fNdiag), fPtr(trc.fPtr) { }
   TMatrixTDiag_const<Element>& operator=(const TMatrixTDiag_const<Element>& trc) {
      if(this != &trc) { fMatrix=trc.fMatrix; fInc=trc.fInc; fNdiag=trc.fNdiag; fPtr=trc.fPtr; } return *this;}
   virtual ~TMatrixTDiag_const() { }

   inline const TMatrixTBase<Element> *GetMatrix() const { return fMatrix; }
   inline const Element               *GetPtr   () const { return fPtr; }
   inline       Int_t                  GetInc   () const { return fInc; }
   inline const Element               &operator ()(Int_t i) const {
      R__ASSERT(fMatrix->IsValid());
      if (i < fNdiag && i >= 0)
         return fPtr[i*fInc];
      else {
         Error("operator()","Request diagonal(%d) outside matrix range of 0 - %d",i,fNdiag);
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element               &operator [](Int_t i) const { return (*(const TMatrixTDiag_const<Element> *)this)(i); }

   Int_t GetNdiags() const { return fNdiag; }

   ClassDef(TMatrixTDiag_const,0)  // Template of General Matrix Diagonal Access class
};

template<class Element> class TMatrixTDiag : public TMatrixTDiag_const<Element> {

public:
   TMatrixTDiag() {}
   TMatrixTDiag(TMatrixT   <Element>&matrix);
   TMatrixTDiag(TMatrixTSym<Element>&matrix);
   TMatrixTDiag(const TMatrixTDiag<Element> &md);

   inline Element *GetPtr() const { return const_cast<Element *>(this->fPtr); }

   inline const Element &operator()(Int_t i) const {
      R__ASSERT(this->fMatrix->IsValid());
      if (i < this->fNdiag && i >= 0)
         return (this->fPtr)[i*this->fInc];
      else {
         Error("operator()","Request diagonal(%d) outside matrix range of 0 - %d",i,this->fNdiag);
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline       Element &operator()(Int_t i) {
      R__ASSERT(this->fMatrix->IsValid());
      if (i < this->fNdiag && i >= 0)
         return (const_cast<Element *>(this->fPtr))[i*this->fInc];
      else {
         Error("operator()","Request diagonal(%d) outside matrix range of 0 - %d",i,this->fNdiag);
         return (const_cast<Element *>(this->fPtr))[0];
      }
   }
   inline const Element &operator[](Int_t i) const { return (*(const TMatrixTDiag<Element> *)this)(i); }
   inline       Element &operator[](Int_t i)       { return (*(      TMatrixTDiag *)this)(i); }

   void operator= (Element val);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTDiag_const<Element> &d);
   TMatrixTDiag<Element>& operator=(const TMatrixTDiag <Element> &d) { operator=((TMatrixTDiag_const<Element> &)d); return *this;}
   void operator=(const TVectorT          <Element> &vec);

   void operator+=(const TMatrixTDiag_const<Element> &d);
   void operator*=(const TMatrixTDiag_const<Element> &d);

   ClassDef(TMatrixTDiag,0)  // Template of General Matrix Diagonal Access class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTFlat_const                                                   //
//                                                                      //
// Template class represents a flat TMatrixT/TMatrixTSym                //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTFlat_const {

protected:
   const TMatrixTBase<Element> *fMatrix;  //  the matrix I am the diagonal of
         Int_t                  fNelems;  //
   const Element               *fPtr;     //  pointer to the a[0,0]

public:
   TMatrixTFlat_const() { fMatrix = 0; fNelems = 0; fPtr = 0; }
   TMatrixTFlat_const(const TMatrixT   <Element> &matrix);
   TMatrixTFlat_const(const TMatrixTSym<Element> &matrix);
   TMatrixTFlat_const(const TMatrixTFlat_const<Element>& trc):
     fMatrix(trc.fMatrix), fNelems(trc.fNelems), fPtr(trc.fPtr) { }
   TMatrixTFlat_const<Element>& operator=(const TMatrixTFlat_const<Element>& trc) {
      if(this != &trc) { fMatrix=trc.fMatrix; fNelems=trc.fNelems; fPtr=trc.fPtr; } return *this;}
   virtual ~TMatrixTFlat_const() { }

   inline const TMatrixTBase<Element> *GetMatrix() const { return fMatrix; }
   inline const Element               *GetPtr   () const { return fPtr; }
   inline const Element               &operator ()(Int_t i) const {
      R__ASSERT(fMatrix->IsValid());
      if (i < fNelems && i >= 0)
         return fPtr[i];
      else {
         Error("operator()","Request element(%d) outside matrix range of 0 - %d",i,fNelems);
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element               &operator [](Int_t i) const { return (*(const TMatrixTFlat_const<Element> *)this)(i); }

   ClassDef(TMatrixTFlat_const,0)  // Template of General Matrix Flat Representation class
};

template<class Element> class TMatrixTFlat : public TMatrixTFlat_const<Element> {

public:
   TMatrixTFlat() {}
   TMatrixTFlat(TMatrixT   <Element> &matrix);
   TMatrixTFlat(TMatrixTSym<Element> &matrix);
   TMatrixTFlat(const TMatrixTFlat<Element> &mf);

   inline Element *GetPtr() const { return const_cast<Element *>(this->fPtr); }

   inline const Element &operator()(Int_t i) const {
      R__ASSERT(this->fMatrix->IsValid());
      if (i < this->fNelems && i >= 0)
         return (this->fPtr)[i];
      else {
         Error("operator()","Request element(%d) outside matrix range of 0 - %d",i,this->fNelems);
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline       Element &operator()(Int_t i) {
      R__ASSERT(this->fMatrix->IsValid());
      if (i < this->fNelems && i >= 0)
         return (const_cast<Element *>(this->fPtr))[i];
      else {
         Error("operator()","Request element(%d) outside matrix range of 0 - %d",i,this->fNelems);
         return TMatrixTBase<Element>::NaNValue();
      }
   }
   inline const Element &operator[](Int_t i) const { return (*(const TMatrixTFlat<Element> *)this)(i); }
   inline       Element &operator[](Int_t i)       { return (*(      TMatrixTFlat<Element> *)this)(i); }

   void operator= (Element val);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTFlat_const<Element> &f);
   TMatrixTFlat<Element>& operator=(const TMatrixTFlat <Element> &f) { operator=((TMatrixTFlat_const<Element> &)f); return *this;}
   void operator=(const TVectorT          <Element> &vec);

   void operator+=(const TMatrixTFlat_const<Element> &f);
   void operator*=(const TMatrixTFlat_const<Element> &f);

   ClassDef(TMatrixTFlat,0)  // Template of General Matrix Flat Representation class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTSub_const                                                    //
//                                                                      //
// Template class represents a sub matrix of TMatrixT/TMatrixTSym       //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTSub_const {

protected:
   const TMatrixTBase<Element> *fMatrix;    //  the matrix I am a submatrix of
         Int_t                  fRowOff;    //
         Int_t                  fColOff;    //
         Int_t                  fNrowsSub;  //
         Int_t                  fNcolsSub;  //

public:
   TMatrixTSub_const() { fRowOff = fColOff = fNrowsSub = fNcolsSub = 0; fMatrix = 0; }
   TMatrixTSub_const(const TMatrixT   <Element> &matrix,Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
   TMatrixTSub_const(const TMatrixTSym<Element> &matrix,Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
   virtual ~TMatrixTSub_const() { }

   inline const TMatrixTBase<Element> *GetMatrix() const { return fMatrix; }
   inline       Int_t                  GetRowOff() const { return fRowOff; }
   inline       Int_t                  GetColOff() const { return fColOff; }
   inline       Int_t                  GetNrows () const { return fNrowsSub; }
   inline       Int_t                  GetNcols () const { return fNcolsSub; }
   inline const Element               &operator ()(Int_t rown,Int_t coln) const {
      R__ASSERT(fMatrix->IsValid());

      const Element *ptr = fMatrix->GetMatrixArray();
      if (rown >= fNrowsSub || rown < 0) {
         Error("operator()","Request row(%d) outside matrix range of 0 - %d",rown,fNrowsSub);
         return TMatrixTBase<Element>::NaNValue();
      }
      if (coln >= fNcolsSub || coln < 0) {
         Error("operator()","Request column(%d) outside matrix range of 0 - %d",coln,fNcolsSub);
         return TMatrixTBase<Element>::NaNValue();
      }
      const Int_t index = (rown+fRowOff)*fMatrix->GetNcols()+coln+fColOff;
      return ptr[index];
   }

   ClassDef(TMatrixTSub_const,0)  // Template of Sub Matrix Access class
};

template<class Element> class TMatrixTSub : public TMatrixTSub_const<Element> {

public:

   enum {kWorkMax = 100};

   TMatrixTSub() {}
   TMatrixTSub(TMatrixT   <Element> &matrix,Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
   TMatrixTSub(TMatrixTSym<Element> &matrix,Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
   TMatrixTSub(const TMatrixTSub<Element> &ms);

   inline Element &operator()(Int_t rown,Int_t coln) {
      R__ASSERT(this->fMatrix->IsValid());

      const Element *ptr = this->fMatrix->GetMatrixArray();
      if (rown >= this->fNrowsSub || rown < 0) {
         Error("operator()","Request row(%d) outside matrix range of 0 - %d",rown,this->fNrowsSub);
         return TMatrixTBase<Element>::NaNValue();
      }
      if (coln >= this->fNcolsSub || coln < 0) {
         Error("operator()","Request column(%d) outside matrix range of 0 - %d",coln,this->fNcolsSub);
         return TMatrixTBase<Element>::NaNValue();
      }
      const Int_t index = (rown+this->fRowOff)*this->fMatrix->GetNcols()+coln+this->fColOff;
      return (const_cast<Element *>(ptr))[index];
   }

   void Rank1Update(const TVectorT<Element> &vec,Element alpha=1.0);

   void operator= (Element val);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTSub_const<Element> &s);
   TMatrixTSub<Element>& operator=(const TMatrixTSub <Element> &s) { operator=((TMatrixTSub_const<Element> &)s); return *this;}
   void operator=(const TMatrixTBase     <Element> &m);

   void operator+=(const TMatrixTSub_const<Element> &s);
   void operator*=(const TMatrixTSub_const<Element> &s);
   void operator+=(const TMatrixTBase     <Element> &m);
   void operator*=(const TMatrixT         <Element> &m);
   void operator*=(const TMatrixTSym      <Element> &m);

   ClassDef(TMatrixTSub,0)  // Template of Sub Matrix Access class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTSparseRow_const                                              //
//                                                                      //
// Template class represents a row of TMatrixTSparse                    //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTSparseRow_const {

protected:
   const TMatrixTSparse<Element> *fMatrix;  // the matrix I am a row of
         Int_t                  fRowInd;  // effective row index
         Int_t                  fNindex;  // index range
   const Int_t                 *fColPtr;  // column index pointer
   const Element               *fDataPtr; // data pointer

public:
   TMatrixTSparseRow_const() { fMatrix = 0; fRowInd = 0; fNindex = 0; fColPtr = 0; fDataPtr = 0; }
   TMatrixTSparseRow_const(const TMatrixTSparse<Element> &matrix,Int_t row);
   TMatrixTSparseRow_const(const TMatrixTSparseRow_const<Element>& trc):
     fMatrix(trc.fMatrix), fRowInd(trc.fRowInd), fNindex(trc.fNindex), fColPtr(trc.fColPtr), fDataPtr(trc.fDataPtr) { }
   TMatrixTSparseRow_const<Element>& operator=(const TMatrixTSparseRow_const<Element>& trc) {
     if(this != &trc) { fMatrix=trc.fMatrix; fRowInd=trc.fRowInd; fNindex=trc.fNindex; fColPtr=trc.fColPtr; fDataPtr=trc.fDataPtr; }  return *this;}
   virtual ~TMatrixTSparseRow_const() { }

   inline const TMatrixTBase<Element> *GetMatrix  () const { return fMatrix; }
   inline const Element               *GetDataPtr () const { return fDataPtr; }
   inline const Int_t                 *GetColPtr  () const { return fColPtr; }
   inline       Int_t                  GetRowIndex() const { return fRowInd; }
   inline       Int_t                  GetNindex  () const { return fNindex; }

          Element operator()(Int_t i) const;
   inline Element operator[](Int_t i) const { return (*(const TMatrixTSparseRow_const<Element> *)this)(i); }

   ClassDef(TMatrixTSparseRow_const,0)  // Template of Sparse Matrix Row Access class
};

template<class Element> class TMatrixTSparseRow : public TMatrixTSparseRow_const<Element> {

public:
   TMatrixTSparseRow() {}
   TMatrixTSparseRow(TMatrixTSparse<Element> &matrix,Int_t row);
   TMatrixTSparseRow(const TMatrixTSparseRow<Element> &mr);

   inline Element *GetDataPtr() const { return const_cast<Element *>(this->fDataPtr); }

          Element  operator()(Int_t i) const;
          Element &operator()(Int_t i);
   inline Element  operator[](Int_t i) const { return (*(const TMatrixTSparseRow<Element> *)this)(i); }
   inline Element &operator[](Int_t i)       { return (*(TMatrixTSparseRow<Element> *)this)(i); }

   void operator= (Element val);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTSparseRow_const<Element> &r);
   TMatrixTSparseRow<Element>& operator=(const TMatrixTSparseRow <Element> &r) { operator=((TMatrixTSparseRow_const<Element> &)r); return *this;}
   void operator=(const TVectorT               <Element> &vec);

   void operator+=(const TMatrixTSparseRow_const<Element> &r);
   void operator*=(const TMatrixTSparseRow_const<Element> &r);

   ClassDef(TMatrixTSparseRow,0)  // Template of Sparse Matrix Row Access class
};

//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMatrixTSparseDiag_const                                             //
//                                                                      //
// Template class represents the diagonal of TMatrixTSparse             //
//                                                                      //
//////////////////////////////////////////////////////////////////////////

template<class Element> class TMatrixTSparseDiag_const {

protected:
   const TMatrixTSparse<Element> *fMatrix;  //  the matrix I am the diagonal of
         Int_t                  fNdiag;   //  number of diag elems, min(nrows,ncols)
   const Element               *fDataPtr; //  data pointer

public:
   TMatrixTSparseDiag_const() { fMatrix = 0; fNdiag = 0; fDataPtr = 0; }
   TMatrixTSparseDiag_const(const TMatrixTSparse<Element> &matrix);
   TMatrixTSparseDiag_const(const TMatrixTSparseDiag_const<Element>& trc):
     fMatrix(trc.fMatrix), fNdiag(trc.fNdiag), fDataPtr(trc.fDataPtr) { }
   TMatrixTSparseDiag_const<Element>& operator=(const TMatrixTSparseDiag_const<Element>& trc) {
      if(this !=  &trc) { fMatrix=trc.fMatrix; fNdiag=trc.fNdiag; fDataPtr=trc.fDataPtr; } return *this;}
   virtual ~TMatrixTSparseDiag_const() { }

   inline const TMatrixTBase<Element> *GetMatrix () const { return fMatrix; }
   inline const Element               *GetDataPtr() const { return fDataPtr; }
   inline       Int_t                  GetNdiags () const { return fNdiag; }

          Element operator ()(Int_t i) const;
   inline Element operator [](Int_t i) const { return (*(const TMatrixTSparseRow_const<Element> *)this)(i); }

   ClassDef(TMatrixTSparseDiag_const,0)  // Template of Sparse Matrix Diagonal Access class
};

template<class Element> class TMatrixTSparseDiag : public TMatrixTSparseDiag_const<Element> {

public:
   TMatrixTSparseDiag() {}
   TMatrixTSparseDiag(TMatrixTSparse<Element> &matrix);
   TMatrixTSparseDiag(const TMatrixTSparseDiag<Element> &md);

   inline Element *GetDataPtr() const { return const_cast<Element *>(this->fDataPtr); }

                Element  operator()(Int_t i) const;
                Element &operator()(Int_t i);
   inline       Element  operator[](Int_t i) const { return (*(const TMatrixTSparseDiag<Element> *)this)(i); }
   inline       Element &operator[](Int_t i)       { return (*(TMatrixTSparseDiag<Element> *)this)(i); }

   void operator= (Element val);
   void operator+=(Element val);
   void operator*=(Element val);

   void operator=(const TMatrixTSparseDiag_const<Element> &d);
   TMatrixTSparseDiag<Element>& operator=(const TMatrixTSparseDiag <Element> &d) { operator=((TMatrixTSparseDiag_const<Element> &)d); return *this;}
   void operator=(const TVectorT                <Element> &vec);

   void operator+=(const TMatrixTSparseDiag_const<Element> &d);
   void operator*=(const TMatrixTSparseDiag_const<Element> &d);

   ClassDef(TMatrixTSparseDiag,0)  // Template of Sparse Matrix Diagonal Access class
};

Double_t Drand(Double_t &ix);
#endif